Article
Astronomy & Astrophysics
Denis Boyda, Gurtej Kanwar, Sebastien Racaniere, Danilo Jimenez Rezende, Michael S. Albergo, Kyle Cranmer, Daniel C. Hackett, Phiala E. Shanahan
Summary: A flow-based sampling algorithm has been developed for SU(N) lattice gauge theories, ensuring gauge invariance by construction. This algorithm constructs flows on an SU(N) variable (or on a U(N) variable through a simple alternative) that respects matrix conjugation symmetry, and has been applied to sample distributions of single SU(N) variables and to construct flow-based samplers for SU(2) and SU(3) lattice gauge theory in two dimensions.
Article
Astronomy & Astrophysics
Arata Yamamoto
Summary: In this article, we discuss quantum computation of lattice gauge theory using the path integral formalism, utilizing a quantum sampling algorithm to generate gauge configurations, and demonstrating a benchmark test of Z(2) lattice gauge theory on a four-dimensional hypercube.
Article
Astronomy & Astrophysics
C. Lehner, T. Wettig
Summary: We demonstrate that a state-of-the-art multigrid preconditioner can be efficiently learned by gauge-equivariant neural networks. The models require minimal retraining on different gauge configurations and remain efficient under modest modifications of ensemble parameters. Furthermore, important paradigms such as communication avoidance can be straightforwardly implemented in this framework.
Article
Astronomy & Astrophysics
Patrick Emonts, Erez Zohar
Summary: Fermionic Gaussian projected entangled pair states (PEPS) are used to describe ground states of noninteracting fermionic Hamiltonians. They can be efficiently studied and analyzed using both analytical and numerical methods. Recently, they have been used as a starting point for variational study of interacting lattice gauge theories, with the help of PEPS gauging mechanisms and sign-problem free variational Monte Carlo techniques. This work focuses on generalizing such states from two to three spatial dimensions, with a focus on spin representations and lattice rotations, which are crucial for studying nonperturbative lattice gauge theories with fermionic tensor network states.
Article
Multidisciplinary Sciences
Yasar Y. Atas, Jinglei Zhang, Randy Lewis, Amin Jahanpour, Jan F. Haase, Christine A. Muschik
Summary: Researchers utilized quantum computing to simulate non-Abelian gauge theories, uncovering meson and baryon states and laying the groundwork for future quantum simulations.
NATURE COMMUNICATIONS
(2021)
Article
Astronomy & Astrophysics
Srinath Bulusu, Matteo Favoni, Andreas Ipp, David Mueller, Daniel Schuh
Summary: The study investigates the advantages of using group equivariant convolutional neural networks in complex scalar field theory on a two-dimensional lattice in high-energy physics and lattice field theory. The results demonstrate that equivariant architectures generally outperform their nonequivariant counterparts in regression and classification tasks, showing better performance and generalizability.
Article
Physics, Multidisciplinary
Salvatore D. Pace, Siddhardh C. Morampudi, Roderich Moessner, Chris R. Laumann
Summary: Quantum spin ice, as a unique condensed-matter system, displays significant differences in microstructure and parameters from standard quantum electrodynamics, with parameters tunable by adjusting the microscopic Hamiltonian. Its high fine structure constant implies that experiments may observe phenomena arising from strong interactions.
PHYSICAL REVIEW LETTERS
(2021)
Article
Mathematics, Applied
Bo Liu
Summary: This paper investigates the anomaly formula and functoriality of equivariant Bismut-Cheeger eta forms with perturbation operators for a compact Lie group action, and constructs a new analytic model for the equivariant differential K-theory on compact manifolds with finite stabilizers. The results provide insights on the well-definedness of the push-forward map, addressing a question raised by Bunke and Schick (2009).
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Quantum Science & Technology
Yanting Cheng, Shang Liu, Wei Zheng, Pengfei Zhang, Hui Zhai
Summary: This article introduces the realization of the one-dimensional lattice Schwinger model using bosons and Rydberg-atom arrays, and discusses methods to study confinement and deconfinement by varying the mass of the matter field and tuning the topological angle.
Article
Astronomy & Astrophysics
M. G. Echevarria, I. L. Egusquiza, E. Rico, G. Schnell
Summary: This paper introduces a quantum algorithm for performing quantum simulation of different nonperturbative parton correlators in high-energy collider physics, illustrated by considering a space-time Wilson loop, and discusses the implementation of the algorithm in actual quantum technologies.
Article
Physics, Multidisciplinary
Kanehisa Takasaki
Summary: The intermediate long wave (ILW) hierarchy, formulated as reductions of the lattice KP hierarchy, inherits its integrability and can capture all solutions through a factorization problem of difference operators. A special solution is obtained from Okounkov and Pandharipande's dressing operators for equivariant Gromov-Witten theory, suggesting a hidden link with the equivariant Toda hierarchy. The generalized ILW hierarchy is also related to the lattice Gelfand-Dickey hierarchy and logarithmic flows can be derived from it through a scaling limit.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Review
Physics, Mathematical
Ilya Chevyrev
Summary: We review two works that study the stochastic quantization equations of Yang-Mills on two- and three-dimensional Euclidean space with finite volume. The main result of these works is that one can renormalize the 2D and 3D stochastic Yang-Mills heat flow so that the dynamic becomes gauge covariant in law, and a number of open problems are pointed out.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Multidisciplinary
R. R. Ferguson, L. Dellantonio, A. Al Balushi, K. Jansen, W. Dur, C. A. Muschik
Summary: This approach utilizes measurement-based quantum computation principles, involving entangled resource states and local measurements, and presents two measurement-based VQE schemes, introducing a new method for constructing variational families and translating circuit-based schemes. Both schemes offer specific advantages in terms of required resources and coherence times.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Jan Horak, Friederike Ihssen, Joannis Papavassiliou, Jan M. Pawlowski, Axel Weber, Christof Wetterich
Summary: In this study, an analytic understanding of the infrared regularization of the gluon propagator in covariant gauges is proposed using lattice simulations and studies in continuum QCD. The phenomenon is explained in terms of gluon condensation through a dynamical version of the Higgs mechanism, resulting in the emergence of color condensates. The effective potential of covariantly constant field strengths is computed using the functional renormalization group approach, and the non-trivial minimum of the potential is related to the color condensates. The obtained gluon mass value is found to be consistent with lattice results and other dynamical scenarios.
Article
Mathematics, Applied
Zhenning Cai, Xiaoyu Dong, Yang Kuang
Summary: Through in-depth analysis of the complex Langevin method and its limitations, we reveal that the absence of localized probability density functions leads to unstable behavior, while the gauge cooling technique helps confine samples in certain cases, significantly broadening its application.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Multidisciplinary Sciences
Peter Lunts, Michael S. Albergo, Michael Lindsey
Summary: A quantum critical point (QCP) is believed to be a key component in the phase diagram of iron-based superconductors and electron-doped cuprates. The authors numerically study a spin-fermion model and extract the scaling exponents and functional form of the spin susceptibility using a Hybrid Monte Carlo (HMC) algorithm. Their findings contradict previous results and suggest that the universal scaling is governed by a fixed point discovered near perfect nesting.
NATURE COMMUNICATIONS
(2023)
Article
Astronomy & Astrophysics
A. Avkhadiev, P. E. Shanahan, R. D. Young
Summary: It has been suggested that noisy intermediate-scale quantum computers can optimize interpolating operator constructions in lattice quantum field theory (LQFT) calculations. In this study, two specific methods were developed and implemented. The first method maximizes the fidelity between the state created by an interpolating operator and the target eigenstate, while the second method minimizes the energy expectation value of the interpolated state. These methods were applied in a proof-of-concept calculation for a single-flavor massive Schwinger model in (1 thorn 1) dimensions to obtain quantum-optimized interpolating operator constructions for a vector meson state. The results showed that energy minimization is more robust to quantum gate errors in the proof-of-concept calculation. This work demonstrates how intermediate-term quantum computers can accelerate classical LQFT calculations.
Article
Astronomy & Astrophysics
Salvatore Cali, Daniel C. Hackett, Yin Lin, Phiala E. Shanahan, Brian Xiao
Summary: This work develops neural-network-based preconditioners to accelerate the convergence of the conjugate gradient solver in lattice quantum field theories. It shows that these neural-network preconditioners outperform other conventional preconditioning approaches, such as even-odd or incomplete Cholesky decompositions, in terms of reducing the number of iterations and complex operations required for convergence. Additionally, a volume-transferring technique is introduced to enable the use of small lattice volumes for training preconditioners in ensembles with larger lattice volumes, without significant performance degradation.
Article
Astronomy & Astrophysics
Michael S. Albergo, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Gurtej Kanwar, Sebastien Racaniere, Danilo J. Rezende, Fernando Romero-Lopez, Phiala E. Shanahan, Julian M. Urban
Summary: Recent results suggest that flow-based algorithms are efficient for sampling field distributions in lattice field theory applications. This study provides a numerical demonstration on the robustness of flow-based sampling in the Schwinger model at the critical fermion mass value. Conventional methods, on the other hand, fail to sample all parts of configuration space and lead to significantly underestimated uncertainties.
Article
Astronomy & Astrophysics
Ryan Abbott, Michael S. Albergo, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Gurtej Kanwar, Sebastien Racaniere, Danilo J. Rezende, Fernando Romero-Lopez, Phiala E. Shanahan, Betsy Tian, Julian M. Urban
Summary: This work introduces gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories, using pseudofermions as stochastic estimators for the fermionic determinant. The methods of improving flow-based sampling approaches through standard techniques are also outlined. Numerical demonstrations are provided in two-dimensional U(1) and SU(3) gauge theories with Nf 1/4 2 flavors of fermions.
Article
Astronomy & Astrophysics
Xiangkai Sun, William Detmold, Di Luo, Phiala E. Shanahan
Summary: Finite-volume pionless effective field theory provides an efficient framework for extrapolating nuclear spectra and matrix elements from finite volume to infinite volume, as well as for extending calculations to larger atomic systems. In this work, the authors demonstrate the implementation of this framework using optimized correlated Gaussian wave functions and solving a generalized eigenvalue problem, which is shown to be significantly more efficient compared to previous stochastic methods.
Article
Astronomy & Astrophysics
Dimitra A. Pefkou, Daniel C. Hackett, Phiala E. Shanahan
Summary: The lattice QCD study investigates the gluon gravitational form factors of hadrons, revealing their contributions to various mechanical properties and estimating corresponding mechanical and mass radii. The results provide insights into the internal structure of hadrons and the role of gluons.
Article
Astronomy & Astrophysics
Michael S. Albergo, Gurtej Kanwar, Sebastien Racaniere, Danilo J. Rezende, Julian M. Urban, Denis Boyda, Kyle Cranmer, Daniel C. Hackett, Phiala E. Shanahan
Summary: Algorithms based on normalizing flows are seen as promising machine learning methods for sampling complex probability distributions. Studies have demonstrated their effectiveness in scalar theories, gauge theories, and statistical systems, while developing approaches for sampling theories with dynamical fermions. These methods have been applied to the sampling of field configurations in a two-dimensional theory involving massless staggered fermions and a scalar field with Yukawa interaction.
Article
Astronomy & Astrophysics
Assumpta Parreno, Phiala E. Shanahan, Michael L. Wagman, Frank Winter, Emmanuel Chang, William Detmold, Marc Illa
Summary: This study investigates the axial charge of the triton using lattice QCD, finding a compact bound state with the quantum numbers of the triton at specific quark masses, and a triton to proton axial charge ratio of 0.91. Results from correlation functions calculations and FVEFT extrapolation show that QCD can explain the modification to the triton's axial charge.
Article
Astronomy & Astrophysics
W. Detmold, P. E. Shanahan
Summary: The study investigates the use of pionless effective field theory in a finite volume (FVEFT pi/) as a framework to analyze multinucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT pi/ with the stochastic variational method, spectra of nuclei with atomic number A is an element of {2, 3} are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses, enabling determination of infinite-volume binding energies.
Article
Astronomy & Astrophysics
Denis Boyda, Gurtej Kanwar, Sebastien Racaniere, Danilo Jimenez Rezende, Michael S. Albergo, Kyle Cranmer, Daniel C. Hackett, Phiala E. Shanahan
Summary: A flow-based sampling algorithm has been developed for SU(N) lattice gauge theories, ensuring gauge invariance by construction. This algorithm constructs flows on an SU(N) variable (or on a U(N) variable through a simple alternative) that respects matrix conjugation symmetry, and has been applied to sample distributions of single SU(N) variables and to construct flow-based samplers for SU(2) and SU(3) lattice gauge theory in two dimensions.
